How exactly does MICE imputation combine multiple datasets into one?
MICE is a Multiple imputation method, it contains three phases:

Imputation phase: The missing data are estimated M times from a specific model to obtain M complete and potentially different data sets.
Separate analysis phase: The selected analysis is performed separately on each of m = 1, ..., M sets of imputed data to obtain estimates (central tendency and variance).
Combined analysis phase: The results obtained  are combined according to the rules established by Rubin to obtain a single final estimate.